Question

​Combined, there are ​Asians, Africans,​ Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by . The difference between the number of Europeans and Americans is . If the number of Africans is​ doubled, their population exceeds the number of Europeans and Americans by . Determine the number of​ Asians, Africans,​ Europeans, and Americans in this village

Answer 1

There are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

To determine the number of Asians, Africans, Europeans, and Americans in the village, the following calculation must be performed:

 

• A.S + A.F + E.U + A.M = 177
• A.S = A.F + E.U + 69
• E.U - A.M = 13
• E.U = A.M + 13
• 2A.F = E.U + A.M + 29
• A.F + E.U + 69 + A.F + E.U + A.M = 177
• A.F + A.M + 13 + 69 + A.F + A.M + 13 + A.M = 177
• 2A.F + 3A.M = 177 - 13 - 13 - 69
• E.U + A.M + 29 + 3A.M = 82
• A.M + 13 + A.M + 29 + 3A.M = 82
• 5A.M = 82 - 13 - 29
• A.M = 40/5
• A.M = 8
• E.U = 8 + 13 = 21
• A.F = (21 + 29) / 2 = 25
• A.S = 177 - 25 - 21 - 8 = 123

Therefore, there are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

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